A Rate Equation Approach to Elucidate the Kinetics and Robustness of the TGF-β Pathway

We present a rate equation model for the TGF-β pathway in endothelial cells together with novel measurements. This pathway plays a prominent role in inter- and intracellular communication and subversion can lead to cancer, fibrosis vascular disorders, and immune diseases. The model successfully describes the kinetics of experimental data and also correctly predicts the behavior in experiments where the system is perturbed. A novel method in this context, simulated tempering, is used to fit the model parameters to the data. It provides an ensemble of high quality solutions, which are analyzed with clustering methods and display a hierarchical structure highlighting distinct parameter subspaces with biological interpretations. This analysis discriminates between different biological mechanisms to achieve a transient signal from a sustained TGF-β input, where one mechanism is to use a negative feedback to turn the signal off. Further analysis in terms of parameter sensitivity reveals that this negative feedback loop in TGF-β signaling renders the system global robustness. This sheds light upon the role of the Smad7 protein in this system.